Abstract
As revealed by the no free lunch theorem, no single algorithm can outperform any others on all classes of optimization problems. To tackle this issue, methods for recommending an existing algorithm for solving given problems have been proposed. However, existing recommendation methods for continuous optimization suffer from low practicability and transferability, mainly due to the difficulty in extracting features that can effectively describe the problem structure and lack of data for training a recommendation model. This work proposes a generic recommender system to address the above two challenges. First, a novel method is proposed to represent an analytic objective function of a continuous optimization problem as a tree, which is directly used as the features of the problem. For black-box optimization problems whose objective function is unknown, a symbolic regressor is adopted to estimate the tree structure. Second, a large number of benchmark problems are randomly created based on the proposed tree representation, providing an abundant amount of training data with various levels of difficulty. By employing a deep recurrent neural network, a recommendation model is trained to recommend a most suitable metaheuristic algorithm for white- or black-box optimization, making a significant step forward towards fully automated algorithm recommendation for continuous optimization. Experimental results on 100 000 benchmark problems show that the proposed recommendation model achieves considerably better performance than existing ones, and exhibits high transferability to real-world problems.